Excess attenuation of an acoustic beam by turbulence

A theory based on the concept of a spatial sinusoidal diffraction grating is presented for the estimation of the excess attenuation in an acoustic beam. The equation of the excess attenuation coefficient shows that the excess attenuation of acoustic beam not only depends on the turbulence but also depends on the application parameters such as the beam width, the beam orientation and whether for forward propagation or back scatter propagation. Analysis shows that the excess attenuation appears to have a frequency dependence of cube-root. The expression for the excess attenuation coefficient has been used in the estimations of the temperature structure coefficient, C(T)2, in sodar sounding. The correction of C(T)2 values for excess attenuation reduces their errors greatly. Published profiles of temperature structure coefficient and the velocity structure coefficient in convective conditions are used to test our theory, which is compared with the theory by Brown and Clifford. The excess attenuation due to scattering from turbulence and atmospheric absorption are both taken into account in sodar data processing for deducing the contribution of the lower atmosphere to seeing, which is the sharpness of a telescope image determined by the degree of turbulence in the Earth's atmosphere. The comparison between the contributions of the lowest 300-m layer to seeing with that of the whole atmosphere supports the reasonableness of our estimation of excess attenuation.